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Calculus BC · AP · Differential Equations

CED focus

Sketching Slope Fields

This topic is assessed on the AP Exam.

Multiple-choice tips

  • Match slope-field segments to dy/dx signs in MC.
  • Eliminate separation-of-variables steps that mix x and y incorrectly.
  • Check whether the MC question asks for a family or a particular solution.
  • On growth models, identify carrying capacity vs initial value.

Free-response tips

  • Show separation and integration with +C before applying an initial condition.
  • Sketch one solution curve through a slope-field point consistently.
  • Verify a proposed solution by substituting into the DE.
  • Interpret parameters in logistic or exponential DE models.

Common traps

  • Forgetting +C before applying an initial condition
  • Sketching a solution curve that crosses slope-field inconsistently
  • Treating every DE as separable without checking

Quick checklist

  • [ ] Can separate variables for a basic DE
  • [ ] Can apply an initial condition to find C
  • [ ] Can describe what a slope field shows

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